3,339 research outputs found
Novel Fourier Quadrature Transforms and Analytic Signal Representations for Nonlinear and Non-stationary Time Series Analysis
The Hilbert transform (HT) and associated Gabor analytic signal (GAS)
representation are well-known and widely used mathematical formulations for
modeling and analysis of signals in various applications. In this study, like
the HT, to obtain quadrature component of a signal, we propose the novel
discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine
quadrature transforms (FSQTs), designated as Fourier quadrature transforms
(FQTs). Using these FQTs, we propose sixteen Fourier-Singh analytic signal
(FSAS) representations with following properties: (1) real part of eight FSAS
representations is the original signal and imaginary part is the FCQT of the
real part, (2) imaginary part of eight FSAS representations is the original
signal and real part is the FSQT of the real part, (3) like the GAS, Fourier
spectrum of the all FSAS representations has only positive frequencies, however
unlike the GAS, the real and imaginary parts of the proposed FSAS
representations are not orthogonal to each other. The Fourier decomposition
method (FDM) is an adaptive data analysis approach to decompose a signal into a
set of small number of Fourier intrinsic band functions which are AM-FM
components. This study also proposes a new formulation of the FDM using the
discrete cosine transform (DCT) with the GAS and FSAS representations, and
demonstrate its efficacy for improved time-frequency-energy representation and
analysis of nonlinear and non-stationary time series.Comment: 22 pages, 13 figure
EEG-Based Emotion Recognition Using Regularized Graph Neural Networks
Electroencephalography (EEG) measures the neuronal activities in different
brain regions via electrodes. Many existing studies on EEG-based emotion
recognition do not fully exploit the topology of EEG channels. In this paper,
we propose a regularized graph neural network (RGNN) for EEG-based emotion
recognition. RGNN considers the biological topology among different brain
regions to capture both local and global relations among different EEG
channels. Specifically, we model the inter-channel relations in EEG signals via
an adjacency matrix in a graph neural network where the connection and
sparseness of the adjacency matrix are inspired by neuroscience theories of
human brain organization. In addition, we propose two regularizers, namely
node-wise domain adversarial training (NodeDAT) and emotion-aware distribution
learning (EmotionDL), to better handle cross-subject EEG variations and noisy
labels, respectively. Extensive experiments on two public datasets, SEED and
SEED-IV, demonstrate the superior performance of our model than
state-of-the-art models in most experimental settings. Moreover, ablation
studies show that the proposed adjacency matrix and two regularizers contribute
consistent and significant gain to the performance of our RGNN model. Finally,
investigations on the neuronal activities reveal important brain regions and
inter-channel relations for EEG-based emotion recognition
Jitter-Adaptive Dictionary Learning - Application to Multi-Trial Neuroelectric Signals
Dictionary Learning has proven to be a powerful tool for many image
processing tasks, where atoms are typically defined on small image patches. As
a drawback, the dictionary only encodes basic structures. In addition, this
approach treats patches of different locations in one single set, which means a
loss of information when features are well-aligned across signals. This is the
case, for instance, in multi-trial magneto- or electroencephalography (M/EEG).
Learning the dictionary on the entire signals could make use of the alignement
and reveal higher-level features. In this case, however, small missalignements
or phase variations of features would not be compensated for. In this paper, we
propose an extension to the common dictionary learning framework to overcome
these limitations by allowing atoms to adapt their position across signals. The
method is validated on simulated and real neuroelectric data.Comment: 9 pages, 5 figures, minor correction
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